Central energy system with expert subplant models

ABSTRACT

A central plant includes a plurality of subplants and circuitry. The circuitry is configured to obtain an expert model associated with a first subplant of the plurality of subplants. The expert model includes a map of values of independent variables to one or more dependent variables. The circuitry is also configured to receive input data indicating input values for the independent variables and estimate outputs values for the one or more dependent variables associated with the input variables by determining a spatial relationship between the input data and the expert model, reducing the expert model to a reduced model based on the spatial relationship, and performing an interpolation using the reduced model to generate the output values for the one or more dependent variables. The circuitry is also configured to initiate an automated action using the output values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. Provisional Application No. 63/208,869, filed Jun. 9, 2021, the entire disclosure of which is incorporated by reference herein.

BACKGROUND

The present disclosure relates generally to a central plant or central energy facility configured to serve the energy loads of a building or campus. The present disclosure relates more particular to a central energy system using expert subplant models to generate estimates of building performance for use in executing measurement and validation functions and/or for use in determining an optimal distribution of the energy loads across various subplants of the central plant.

A central plant typically includes multiple subplants configured to serve different types of energy loads. For example, a central plant may include a chiller subplant configured to serve cooling loads, a heater subplant configured to serve heating loads, and/or an electricity subplant configured to serve electric loads. A central plant purchases resources from utilities to run the subplants to meet the loads.

Some central plants include energy storage. Energy storage may be a tank of water that stores hot water for campus heating, an ice tank for campus cooling, and/or battery storage. In the presence of real-time pricing from utilities, it may be advantageous to manipulate the time that a certain resource or energy type is consumed. Instead of producing the resource exactly when it is required by the load, it can be optimal to produce that resource at a time when the production cost is low, store it, and then use it when the resource needed to produce that type of energy is more expensive. It can be difficult and challenging to optimally allocate the energy loads across the assets of the central plant. It can also be difficult and challenging to generate estimates of plant performance, for example to enable comparisons of non-optimal performance to plant performance under optimized control.

SUMMARY

One implementation of the present disclosure is a central plant. The central plant includes a plurality of subplants and circuitry configured to obtain an expert model associated with a first subplant of the plurality of subplants. The expert model comprises a map of values of one or more independent variables characterizing operation of the first subplant to one or more dependent variables characterizing operation of the first subplant. The circuitry is also configured to receive input data indicating input values for the independent variables, and estimate outputs values for the one or more dependent variables associated with the input variables by determining a spatial relationship between the input data and the expert model, reducing the expert model to a reduced model based on the spatial relationship, performing an interpolation using the reduced model to generate the output values for the one or more dependent variables. The circuitry is also configured to initiate an automated action using the output values.

Another implementation of the present disclosure is a method. The method includes obtaining an expert model associated with a first subplant of a central plant. The expert model comprises a map of values of independent variables to one or more dependent variables. The method also includes receiving input data indicating input values for the independent variables and estimating outputs values for the one or more dependent variables associated with the input variables by determining a spatial relationship between the input data and the expert model, reducing the expert model to a reduced model based on the spatial relationship, and performing an interpolation using the reduced model to generate the output values for the one or more dependent variable. The method also includes initiating an automated action using the output values.

Another implementation of the present disclosure is one or more non-transitory computer-readable media storing program instructions that, when executed by one or more processors, cause the one or more processors to perform operations including obtaining an expert model associated with a first subplant of a central plant. The expert model includes a map of values of independent variables to one or more dependent variables. The operations also include receiving input data indicating input values for the independent variables and estimating outputs values for the one or more dependent variables associated with the input variables by determining a spatial relationship between the input data and the expert model, reducing the expert model to a reduced model based on the spatial relationship, and performing an interpolation using the reduced model to generate the output values for the one or more dependent variables. The method also includes initiating an automated action using the output values.

BRIEF DESCRIPTION OF THE DRAWINGS

Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements.

FIG. 1 is a drawing of a building equipped with a HVAC system, according to an exemplary embodiment.

FIG. 2 is a block diagram of a central plant which can be used to serve the energy loads of the building of FIG. 1 , according to an exemplary embodiment.

FIG. 3 is a block diagram of an airside system which can be implemented in the building of FIG. 1 , according to an exemplary embodiment.

FIG. 4 is a block diagram of an asset allocation system including sources, subplants, storage, sinks, and an asset allocator configured to optimize the allocation of these assets, according to according to some embodiments.

FIG. 5 is a block diagram of a central plant controller in which the asset allocator of FIG. 4 can be implemented, according to some embodiments.

FIG. 6 is a flowchart of a process for validation and control using expert subplant models, according to some embodiments.

FIG. 7 is a flowchart of a process for using a spatial relationship between independent data and expert subplant model, according to some embodiments.

FIG. 8 is a diagram of a spatial relationship between independent data and an expert subplant model to illustrate vector math used by the process of FIG. 7 , according to some embodiments.

FIG. 9 is a diagram illustrating an interpolation step used in some embodiments of the process of FIG. 7 , according to some embodiments.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, a central plant with an asset allocator and components thereof are shown, according to various exemplary embodiments. The asset allocator can be configured to manage energy assets such as central plant equipment, battery storage, and other types of equipment configured to serve the energy loads of a building. The asset allocator can determine an optimal distribution of heating, cooling, electricity, and energy loads across different subplants (i.e., equipment groups) of the central plant capable of producing that type of energy.

In some embodiments, the asset allocator is configured to control the distribution, production, storage, and usage of resources in the central plant. The asset allocator can be configured to minimize the economic cost (or maximize the economic value) of operating the central plant over a duration of an optimization period. The economic cost may be defined by a cost function J(x) that expresses economic cost as a function of the control decisions made by the asset allocator. The cost function J(x) may account for the cost of resources purchased from various sources, as well as the revenue generated by selling resources (e.g., to an energy grid) or participating in incentive programs.

The asset allocator can be configured to define various sources, subplants, storage, and sinks. These four categories of objects define the assets of a central plant and their interaction with the outside world. Sources may include commodity markets or other suppliers from which resources such as electricity, water, natural gas, and other resources can be purchased or obtained. Sinks may include the requested loads of a building or campus as well as other types of resource consumers. Subplants are the main assets of a central plant. Subplants can be configured to convert resource types, making it possible to balance requested loads from a building or campus using resources purchased from the sources. Storage can be configured to store energy or other types of resources for later use.

In some embodiments, the asset allocator performs an optimization process to determine an optimal set of control decisions for each time step within the optimization period. The control decisions may include, for example, an optimal amount of each resource to purchase from the sources, an optimal amount of each resource to produce or convert using the subplants, an optimal amount of each resource to store or remove from storage, an optimal amount of each resource to sell to resources purchasers, and/or an optimal amount of each resource to provide to other sinks. In some embodiments, the asset allocator is configured to optimally dispatch all campus energy assets (i.e., the central plant equipment) in order to meet the requested heating, cooling, and electrical loads of the campus for each time step within the optimization period. These and other features of the asset allocator are described in greater detail below.

Building and HVAC System

Referring now to FIG. 1 , a perspective view of a building 10 is shown. Building 10 can be served by a building management system (BMS). A BMS is, in general, a system of devices configured to control, monitor, and manage equipment in or around a building or building area. A BMS can include, for example, a HVAC system, a security system, a lighting system, a fire alerting system, any other system that is capable of managing building functions or devices, or any combination thereof.

The BMS that serves building 10 may include a HVAC system 100. HVAC system 100 can include a plurality of HVAC devices (e.g., heaters, chillers, air handling units, pumps, fans, thermal energy storage, etc.) configured to provide heating, cooling, ventilation, or other services for building 10. For example, HVAC system 100 is shown to include a waterside system 120 and an airside system 130. Waterside system 120 may provide a heated or chilled fluid to an air handling unit of airside system 130. Airside system 130 may use the heated or chilled fluid to heat or cool an airflow provided to building 10. In some embodiments, waterside system 120 can be replaced with or supplemented by a central plant or central energy facility (described in greater detail with reference to FIG. 2 ). An example of an airside system which can be used in HVAC system 100 is described in greater detail with reference to FIG. 3 .

HVAC system 100 is shown to include a chiller 102, a boiler 104, and a rooftop air handling unit (AHU) 106. Waterside system 120 may use boiler 104 and chiller 102 to heat or cool a working fluid (e.g., water, glycol, etc.) and may circulate the working fluid to AHU 106. In various embodiments, the HVAC devices of waterside system 120 can be located in or around building 10 (as shown in FIG. 1 ) or at an offsite location such as a central plant (e.g., a chiller plant, a steam plant, a heat plant, etc.). The working fluid can be heated in boiler 104 or cooled in chiller 102, depending on whether heating or cooling is required in building 10. Boiler 104 may add heat to the circulated fluid, for example, by burning a combustible material (e.g., natural gas) or using an electric heating element. Chiller 102 may place the circulated fluid in a heat exchange relationship with another fluid (e.g., a refrigerant) in a heat exchanger (e.g., an evaporator) to absorb heat from the circulated fluid. The working fluid from chiller 102 and/or boiler 104 can be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship with an airflow passing through AHU 106 (e.g., via one or more stages of cooling coils and/or heating coils). The airflow can be, for example, outside air, return air from within building 10, or a combination of both. AHU 106 may transfer heat between the airflow and the working fluid to provide heating or cooling for the airflow. For example, AHU 106 can include one or more fans or blowers configured to pass the airflow over or through a heat exchanger containing the working fluid. The working fluid may then return to chiller 102 or boiler 104 via piping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e., the supply airflow) to building 10 via air supply ducts 112 and may provide return air from building 10 to AHU 106 via air return ducts 114. In some embodiments, airside system 130 includes multiple variable air volume (VAV) units 116. For example, airside system 130 is shown to include a separate VAV unit 116 on each floor or zone of building 10. VAV units 116 can include dampers or other flow control elements that can be operated to control an amount of the supply airflow provided to individual zones of building 10. In other embodiments, airside system 130 delivers the supply airflow into one or more zones of building 10 (e.g., via supply ducts 112) without using intermediate VAV units 116 or other flow control elements. AHU 106 can include various sensors (e.g., temperature sensors, pressure sensors, etc.) configured to measure attributes of the supply airflow. AHU 106 may receive input from sensors located within AHU 106 and/or within the building zone and may adjust the flow rate, temperature, or other attributes of the supply airflow through AHU 106 to achieve setpoint conditions for the building zone.

Central Plant

Referring now to FIG. 2 , a block diagram of a central plant 200 is shown, according to some embodiments. In various embodiments, central plant 200 can supplement or replace waterside system 120 in HVAC system 100 or can be implemented separate from HVAC system 100. When implemented in HVAC system 100, central plant 200 can include a subset of the HVAC devices in HVAC system 100 (e.g., boiler 104, chiller 102, pumps, valves, etc.) and may operate to supply a heated or chilled fluid to AHU 106. The HVAC devices of central plant 200 can be located within building 10 (e.g., as components of waterside system 120) or at an offsite location such as a central energy facility that serves multiple buildings.

Central plant 200 is shown to include a plurality of subplants 202-208. Subplants 202-208 can be configured to convert energy or resource types (e.g., water, natural gas, electricity, etc.). For example, subplants 202-208 are shown to include a heater subplant 202, a heat recovery chiller subplant 204, a chiller subplant 206, and a cooling tower subplant 208. In some embodiments, subplants 202-208 consume resources purchased from utilities to serve the energy loads (e.g., hot water, cold water, electricity, etc.) of a building or campus. For example, heater subplant 202 can be configured to heat water in a hot water loop 214 that circulates the hot water between heater subplant 202 and building 10. Similarly, chiller subplant 206 can be configured to chill water in a cold water loop 216 that circulates the cold water between chiller subplant 206 building 10.

Heat recovery chiller subplant 204 can be configured to transfer heat from cold water loop 216 to hot water loop 214 to provide additional heating for the hot water and additional cooling for the cold water. Condenser water loop 218 may absorb heat from the cold water in chiller subplant 206 and reject the absorbed heat in cooling tower subplant 208 or transfer the absorbed heat to hot water loop 214. In various embodiments, central plant 200 can include an electricity subplant (e.g., one or more electric generators) configured to generate electricity or any other type of subplant configured to convert energy or resource types.

Hot water loop 214 and cold water loop 216 may deliver the heated and/or chilled water to air handlers located on the rooftop of building 10 (e.g., AHU 106) or to individual floors or zones of building 10 (e.g., VAV units 116). The air handlers push air past heat exchangers (e.g., heating coils or cooling coils) through which the water flows to provide heating or cooling for the air. The heated or cooled air can be delivered to individual zones of building 10 to serve thermal energy loads of building 10. The water then returns to subplants 202-208 to receive further heating or cooling.

Although subplants 202-208 are shown and described as heating and cooling water for circulation to a building, it is understood that any other type of working fluid (e.g., glycol, CO₂, etc.) can be used in place of or in addition to water to serve thermal energy loads. In other embodiments, subplants 202-208 may provide heating and/or cooling directly to the building or campus without requiring an intermediate heat transfer fluid. These and other variations to central plant 200 are within the teachings of the present disclosure.

Each of subplants 202-208 can include a variety of equipment configured to facilitate the functions of the subplant. For example, heater subplant 202 is shown to include a plurality of heating elements 220 (e.g., boilers, electric heaters, etc.) configured to add heat to the hot water in hot water loop 214. Heater subplant 202 is also shown to include several pumps 222 and 224 configured to circulate the hot water in hot water loop 214 and to control the flow rate of the hot water through individual heating elements 220. Chiller subplant 206 is shown to include a plurality of chillers 232 configured to remove heat from the cold water in cold water loop 216. Chiller subplant 206 is also shown to include several pumps 234 and 236 configured to circulate the cold water in cold water loop 216 and to control the flow rate of the cold water through individual chillers 232.

Heat recovery chiller subplant 204 is shown to include a plurality of heat recovery heat exchangers 226 (e.g., refrigeration circuits) configured to transfer heat from cold water loop 216 to hot water loop 214. Heat recovery chiller subplant 204 is also shown to include several pumps 228 and 230 configured to circulate the hot water and/or cold water through heat recovery heat exchangers 226 and to control the flow rate of the water through individual heat recovery heat exchangers 226. Cooling tower subplant 208 is shown to include a plurality of cooling towers 238 configured to remove heat from the condenser water in condenser water loop 218. Cooling tower subplant 208 is also shown to include several pumps 240 configured to circulate the condenser water in condenser water loop 218 and to control the flow rate of the condenser water through individual cooling towers 238.

In some embodiments, one or more of the pumps in central plant 200 (e.g., pumps 222, 224, 228, 230, 234, 236, and/or 240) or pipelines in central plant 200 include an isolation valve associated therewith. Isolation valves can be integrated with the pumps or positioned upstream or downstream of the pumps to control the fluid flows in central plant 200. In various embodiments, central plant 200 can include more, fewer, or different types of devices and/or subplants based on the particular configuration of central plant 200 and the types of loads served by central plant 200.

Still referring to FIG. 2 , central plant 200 is shown to include hot thermal energy storage (TES) 210 and cold thermal energy storage (TES) 212. Hot TES 210 and cold TES 212 can be configured to store hot and cold thermal energy for subsequent use. For example, hot TES 210 can include one or more hot water storage tanks 242 configured to store the hot water generated by heater subplant 202 or heat recovery chiller subplant 204. Hot TES 210 may also include one or more pumps or valves configured to control the flow rate of the hot water into or out of hot TES tank 242.

Similarly, cold TES 212 can include one or more cold water storage tanks 244 configured to store the cold water generated by chiller subplant 206 or heat recovery chiller subplant 204. Cold TES 212 may also include one or more pumps or valves configured to control the flow rate of the cold water into or out of cold TES tanks 244. In some embodiments, central plant 200 includes electrical energy storage (e.g., one or more batteries) or any other type of device configured to store resources. The stored resources can be purchased from utilities, generated by central plant 200, or otherwise obtained from any source.

Airside System

Referring now to FIG. 3 , a block diagram of an airside system 300 is shown, according to some embodiments. In various embodiments, airside system 300 may supplement or replace airside system 130 in HVAC system 100 or can be implemented separate from HVAC system 100. When implemented in HVAC system 100, airside system 300 can include a subset of the HVAC devices in HVAC system 100 (e.g., AHU 106, VAV units 116, ducts 112-114, fans, dampers, etc.) and can be located in or around building 10. Airside system 300 may operate to heat or cool an airflow provided to building 10 using a heated or chilled fluid provided by central plant 200.

Airside system 300 is shown to include an economizer-type air handling unit (AHU) 302. Economizer-type AHUs vary the amount of outside air and return air used by the air handling unit for heating or cooling. For example, AHU 302 may receive return air 304 from building zone 306 via return air duct 308 and may deliver supply air 310 to building zone 306 via supply air duct 312. In some embodiments, AHU 302 is a rooftop unit located on the roof of building 10 (e.g., AHU 106 as shown in FIG. 1 ) or otherwise positioned to receive both return air 304 and outside air 314. AHU 302 can be configured to operate exhaust air damper 316, mixing damper 318, and outside air damper 320 to control an amount of outside air 314 and return air 304 that combine to form supply air 310. Any return air 304 that does not pass through mixing damper 318 can be exhausted from AHU 302 through exhaust damper 316 as exhaust air 322.

Each of dampers 316-320 can be operated by an actuator. For example, exhaust air damper 316 can be operated by actuator 324, mixing damper 318 can be operated by actuator 326, and outside air damper 320 can be operated by actuator 328. Actuators 324-328 may communicate with an AHU controller 330 via a communications link 332. Actuators 324-328 may receive control signals from AHU controller 330 and may provide feedback signals to AHU controller 330. Feedback signals can include, for example, an indication of a current actuator or damper position, an amount of torque or force exerted by the actuator, diagnostic information (e.g., results of diagnostic tests performed by actuators 324-328), status information, commissioning information, configuration settings, calibration data, and/or other types of information or data that can be collected, stored, or used by actuators 324-328. AHU controller 330 can be an economizer controller configured to use one or more control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, feedback control algorithms, etc.) to control actuators 324-328.

Still referring to FIG. 3 , AHU 302 is shown to include a cooling coil 334, a heating coil 336, and a fan 338 positioned within supply air duct 312. Fan 338 can be configured to force supply air 310 through cooling coil 334 and/or heating coil 336 and provide supply air 310 to building zone 306. AHU controller 330 may communicate with fan 338 via communications link 340 to control a flow rate of supply air 310. In some embodiments, AHU controller 330 controls an amount of heating or cooling applied to supply air 310 by modulating a speed of fan 338.

Cooling coil 334 may receive a chilled fluid from central plant 200 (e.g., from cold water loop 216) via piping 342 and may return the chilled fluid to central plant 200 via piping 344. Valve 346 can be positioned along piping 342 or piping 344 to control a flow rate of the chilled fluid through cooling coil 334. In some embodiments, cooling coil 334 includes multiple stages of cooling coils that can be independently activated and deactivated (e.g., by AHU controller 330, by BMS controller 366, etc.) to modulate an amount of cooling applied to supply air 310.

Heating coil 336 may receive a heated fluid from central plant 200 (e.g., from hot water loop 214) via piping 348 and may return the heated fluid to central plant 200 via piping 350. Valve 352 can be positioned along piping 348 or piping 350 to control a flow rate of the heated fluid through heating coil 336. In some embodiments, heating coil 336 includes multiple stages of heating coils that can be independently activated and deactivated (e.g., by AHU controller 330, by BMS controller 366, etc.) to modulate an amount of heating applied to supply air 310.

Each of valves 346 and 352 can be controlled by an actuator. For example, valve 346 can be controlled by actuator 354 and valve 352 can be controlled by actuator 356. Actuators 354-356 may communicate with AHU controller 330 via communications links 358-360. Actuators 354-356 may receive control signals from AHU controller 330 and may provide feedback signals to controller 330. In some embodiments, AHU controller 330 receives a measurement of the supply air temperature from a temperature sensor 362 positioned in supply air duct 312 (e.g., downstream of cooling coil 334 and/or heating coil 336). AHU controller 330 may also receive a measurement of the temperature of building zone 306 from a temperature sensor 364 located in building zone 306.

In some embodiments, AHU controller 330 operates valves 346 and 352 via actuators 354-356 to modulate an amount of heating or cooling provided to supply air 310 (e.g., to achieve a setpoint temperature for supply air 310 or to maintain the temperature of supply air 310 within a setpoint temperature range). The positions of valves 346 and 352 affect the amount of heating or cooling provided to supply air 310 by cooling coil 334 or heating coil 336 and may correlate with the amount of energy consumed to achieve a desired supply air temperature. AHU 330 may control the temperature of supply air 310 and/or building zone 306 by activating or deactivating coils 334-336, adjusting a speed of fan 338, or a combination of both.

Still referring to FIG. 3 , airside system 300 is shown to include a building management system (BMS) controller 366 and a client device 368. BMS controller 366 can include one or more computer systems (e.g., servers, supervisory controllers, subsystem controllers, etc.) that serve as system level controllers, application or data servers, head nodes, or master controllers for airside system 300, central plant 200, HVAC system 100, and/or other controllable systems that serve building 10. BMS controller 366 may communicate with multiple downstream building systems or subsystems (e.g., HVAC system 100, a security system, a lighting system, central plant 200, etc.) via a communications link 370 according to like or disparate protocols (e.g., LON, BACnet, etc.). In various embodiments, AHU controller 330 and BMS controller 366 can be separate (as shown in FIG. 3 ) or integrated. In an integrated implementation, AHU controller 330 can be a software module configured for execution by a processor of BMS controller 366.

In some embodiments, AHU controller 330 receives information from BMS controller 366 (e.g., commands, setpoints, operating boundaries, etc.) and provides information to BMS controller 366 (e.g., temperature measurements, valve or actuator positions, operating statuses, diagnostics, etc.). For example, AHU controller 330 may provide BMS controller 366 with temperature measurements from temperature sensors 362-364, equipment on/off states, equipment operating capacities, and/or any other information that can be used by BMS controller 366 to monitor or control a variable state or condition within building zone 306.

Client device 368 can include one or more human-machine interfaces or client interfaces (e.g., graphical user interfaces, reporting interfaces, text-based computer interfaces, client-facing web services, web servers that provide pages to web clients, etc.) for controlling, viewing, or otherwise interacting with HVAC system 100, its subsystems, and/or devices. Client device 368 can be a computer workstation, a client terminal, a remote or local interface, or any other type of user interface device. Client device 368 can be a stationary terminal or a mobile device. For example, client device 368 can be a desktop computer, a computer server with a user interface, a laptop computer, a tablet, a smartphone, a PDA, or any other type of mobile or non-mobile device. Client device 368 may communicate with BMS controller 366 and/or AHU controller 330 via communications link 372.

Asset Allocation System

Referring now to FIG. 4 , a block diagram of an asset allocation system 400 is shown, according to an exemplary embodiment. Asset allocation system 400 can be configured to manage energy assets such as central plant equipment, battery storage, and other types of equipment configured to serve the energy loads of a building. Asset allocation system 400 can determine an optimal distribution of heating, cooling, electricity, and energy loads across different subplants (i.e., equipment groups) capable of producing that type of energy. In some embodiments, asset allocation system 400 is implemented as a component of central plant 200 and interacts with the equipment of central plant 200 in an online operational environment (e.g., performing real-time control of the central plant equipment). In other embodiments, asset allocation system 400 can be implemented as a component of a planning tool (described with reference to FIGS. 7-8 ) and can be configured to simulate the operation of a central plant over a predetermined time period for planning, budgeting, and/or design considerations.

Asset allocation system 400 is shown to include sources 410, subplants 420, storage 430, and sinks 440. These four categories of objects define the assets of a central plant and their interaction with the outside world. Sources 410 may include commodity markets or other suppliers from which resources such as electricity, water, natural gas, and other resources can be purchased or obtained. Sources 410 may provide resources that can be used by asset allocation system 400 to satisfy the demand of a building or campus. For example, sources 410 are shown to include an electric utility 411, a water utility 412, a natural gas utility 413, a photovoltaic (PV) field (e.g., a collection of solar panels), an energy market 415, and source M 416, where M is the total number of sources 410. Resources purchased from sources 410 can be used by subplants 420 to produce generated resources (e.g., hot water, cold water, electricity, steam, etc.), stored in storage 430 for later use, or provided directly to sinks 440.

Subplants 420 are shown to include a heater subplant 421, a chiller subplant 422, a heat recovery chiller subplant 423, a steam subplant 424, an electricity subplant 425, and subplant N, where N is the total number of subplants 420. In some embodiments, subplants 420 include some or all of the subplants of central plant 200, as described with reference to FIG. 2 . For example, subplants 420 can include heater subplant 202, heat recovery chiller subplant 204, chiller subplant 206, and/or cooling tower subplant 208.

Subplants 420 can be configured to convert resource types, making it possible to balance requested loads from the building or campus using resources purchased from sources 410. For example, heater subplant 421 may be configured to generate hot thermal energy (e.g., hot water) by heating water using electricity or natural gas. Chiller subplant 422 may be configured to generate cold thermal energy (e.g., cold water) by chilling water using electricity. Heat recovery chiller subplant 423 may be configured to generate hot thermal energy and cold thermal energy by removing heat from one water supply and adding the heat to another water supply. Steam subplant 424 may be configured to generate steam by boiling water using electricity or natural gas. Electricity subplant 425 may be configured to generate electricity using mechanical generators (e.g., a steam turbine, a gas-powered generator, etc.) or other types of electricity-generating equipment (e.g., photovoltaic equipment, hydroelectric equipment, etc.).

The input resources used by subplants 420 may be provided by sources 410, retrieved from storage 430, and/or generated by other subplants 420. For example, steam subplant 424 may produce steam as an output resource. Electricity subplant 425 may include a steam turbine that uses the steam generated by steam subplant 424 as an input resource to generate electricity. The output resources produced by subplants 420 may be stored in storage 430, provided to sinks 440, and/or used by other subplants 420. For example, the electricity generated by electricity subplant 425 may be stored in electrical energy storage 433, used by chiller subplant 422 to generate cold thermal energy, used to satisfy the electric load 445 of a building, or sold to resource purchasers 441.

Storage 430 can be configured to store energy or other types of resources for later use. Each type of storage within storage 430 may be configured to store a different type of resource. For example, storage 430 is shown to include hot thermal energy storage 431 (e.g., one or more hot water storage tanks), cold thermal energy storage 432 (e.g., one or more cold thermal energy storage tanks), electrical energy storage 433 (e.g., one or more batteries), and resource type P storage 434, where P is the total number of storage 430. In some embodiments, storage 430 include some or all of the storage of central plant 200, as described with reference to FIG. 2 . In some embodiments, storage 430 includes the heat capacity of the building served by the central plant. The resources stored in storage 430 may be purchased directly from sources or generated by subplants 420.

In some embodiments, storage 430 is used by asset allocation system 400 to take advantage of price-based demand response (PBDR) programs. PBDR programs encourage consumers to reduce consumption when generation, transmission, and distribution costs are high. PBDR programs are typically implemented (e.g., by sources 410) in the form of energy prices that vary as a function of time. For example, some utilities may increase the price per unit of electricity during peak usage hours to encourage customers to reduce electricity consumption during peak times. Some utilities also charge consumers a separate demand charge based on the maximum rate of electricity consumption at any time during a predetermined demand charge period.

Advantageously, storing energy and other types of resources in storage 430 allows for the resources to be purchased at times when the resources are relatively less expensive (e.g., during non-peak electricity hours) and stored for use at times when the resources are relatively more expensive (e.g., during peak electricity hours). Storing resources in storage 430 also allows the resource demand of the building or campus to be shifted in time. For example, resources can be purchased from sources 410 at times when the demand for heating or cooling is low and immediately converted into hot or cold thermal energy by subplants 420. The thermal energy can be stored in storage 430 and retrieved at times when the demand for heating or cooling is high. This allows asset allocation system 400 to smooth the resource demand of the building or campus and reduces the maximum required capacity of subplants 420. Smoothing the demand also asset allocation system 400 to reduce the peak electricity consumption, which results in a lower demand charge.

In some embodiments, storage 430 is used by asset allocation system 400 to take advantage of incentive-based demand response (IBDR) programs. IBDR programs provide incentives to customers who have the capability to store energy, generate energy, or curtail energy usage upon request. Incentives are typically provided in the form of monetary revenue paid by sources 410 or by an independent service operator (ISO). IBDR programs supplement traditional utility-owned generation, transmission, and distribution assets with additional options for modifying demand load curves. For example, stored energy can be sold to resource purchasers 441 or an energy grid 442 to supplement the energy generated by sources 410. In some instances, incentives for participating in an IBDR program vary based on how quickly a system can respond to a request to change power output/consumption. Faster responses may be compensated at a higher level. Advantageously, electrical energy storage 433 allows system 400 to quickly respond to a request for electric power by rapidly discharging stored electrical energy to energy grid 442.

Sinks 440 may include the requested loads of a building or campus as well as other types of resource consumers. For example, sinks 440 are shown to include resource purchasers 441, an energy grid 442, a hot water load 443, a cold water load 444, an electric load 445, and sink Q, where Q is the total number of sinks 440. A building may consume various resources including, for example, hot thermal energy (e.g., hot water), cold thermal energy (e.g., cold water), and/or electrical energy. In some embodiments, the resources are consumed by equipment or subsystems within the building (e.g., HVAC equipment, lighting, computers and other electronics, etc.). The consumption of each sink 440 over the optimization period can be supplied as an input to asset allocation system 400 or predicted by asset allocation system 400. Sinks 440 can receive resources directly from sources 410, from subplants 420, and/or from storage 430.

Still referring to FIG. 4 , asset allocation system 400 is shown to include an asset allocator 402. Asset allocator 402 can be implemented as part of a controller, computing system, cloud computing resource, etc., for example as shown in FIG. 5 and described with reference thereto. Asset allocator 402 may be configured to control the distribution, production, storage, and usage of resources in asset allocation system 400. In some embodiments, asset allocator 402 performs an optimization process determine an optimal set of control decisions for each time step within an optimization period. The control decisions may include, for example, an optimal amount of each resource to purchase from sources 410, an optimal amount of each resource to produce or convert using subplants 420, an optimal amount of each resource to store or remove from storage 430, an optimal amount of each resource to sell to resources purchasers 441 or energy grid 440, and/or an optimal amount of each resource to provide to other sinks 440. In some embodiments, the control decisions include an optimal amount of each input resource and output resource for each of subplants 420.

In some embodiments, asset allocator 402 is configured to optimally dispatch all campus energy assets in order to meet the requested heating, cooling, and electrical loads of the campus for each time step within an optimization horizon or optimization period of duration h. Instead of focusing on only the typical HVAC energy loads, the concept is extended to the concept of resource. Throughout this disclosure, the term “resource” is used to describe any type of commodity purchased from sources 410, used or produced by subplants 420, stored or discharged by storage 430, or consumed by sinks 440. For example, water may be considered a resource that is consumed by chillers, heaters, or cooling towers during operation. This general concept of a resource can be extended to chemical processing plants where one of the resources is the product that is being produced by the chemical processing plat.

Asset allocator 402 can be configured to operate the equipment of asset allocation system 400 to ensure that a resource balance is maintained at each time step of the optimization period. This resource balance is shown in the following equation:

Σx _(time)=0∀resources,∀time∈horizon

where the sum is taken over all producers and consumers of a given resource (i.e., all of sources 410, subplants 420, storage 430, and sinks 440) and time is the time index. Each time element represents a period of time during which the resource productions, requests, purchases, etc. are assumed constant. Asset allocator 402 may ensure that this equation is satisfied for all resources regardless of whether that resource is required by the building or campus. For example, some of the resources produced by subplants 420 may be intermediate resources that function only as inputs to other subplants 420.

In some embodiments, the resources balanced by asset allocator 402 include multiple resources of the same type (e.g., multiple chilled water resources, multiple electricity resources, etc.). Defining multiple resources of the same type may allow asset allocator 402 to satisfy the resource balance given the physical constraints and connections of the central plant equipment. For example, suppose a central plant has multiple chillers and multiple cold water storage tanks, with each chiller physically connected to a different cold water storage tank (i.e., chiller A is connected to cold water storage tank A, chiller B is connected to cold water storage tank B, etc.). Given that only one chiller can supply cold water to each cold water storage tank, a different cold water resource can be defined for the output of each chiller. This allows asset allocator 402 to ensure that the resource balance is satisfied for each cold water resource without attempting to allocate resources in a way that is physically impossible (e.g., storing the output of chiller A in cold water storage tank B, etc.).

Asset allocator 402 may be configured to minimize the economic cost (or maximize the economic value) of operating asset allocation system 400 over the duration of the optimization period. The economic cost may be defined by a cost function J(x) that expresses economic cost as a function of the control decisions made by asset allocator 402. The cost function J(x) may account for the cost of resources purchased from sources 410, as well as the revenue generated by selling resources to resource purchasers 441 or energy grid 442 or participating in incentive programs. The cost optimization performed by asset allocator 402 can be expressed as:

$\underset{x}{\arg\min}{J(x)}$

where J(x) is defined as follows:

${J(x)} = {{\sum\limits_{sources}{\sum\limits_{horizon}{cos{t\left( {{purchase_{{resource},{time}}},{time}} \right)}}}} - {\sum\limits_{incentives}{\sum\limits_{horizon}{{revenue}({ReservationAmount})}}}}$

The first term in the cost function J(x) represents the total cost of all resources purchased over the optimization horizon. Resources can include, for example, water, electricity, natural gas, or other types of resources purchased from a utility or other source 410. The second term in the cost function J(x) represents the total revenue generated by participating in incentive programs (e.g., IBDR programs) over the optimization horizon. The revenue may be based on the amount of power reserved for participating in the incentive programs. Accordingly, the total cost function represents the total cost of resources purchased minus any revenue generated from participating in incentive programs.

Each of subplants 420 and storage 430 may include equipment that can be controlled by asset allocator 402 to optimize the performance of asset allocation system 400. Subplant equipment may include, for example, heating devices, chillers, heat recovery heat exchangers, cooling towers, energy storage devices, pumps, valves, and/or other devices of subplants 420 and storage 430. Individual devices of subplants 420 can be turned on or off to adjust the resource production of each subplant 420. In some embodiments, individual devices of subplants 420 can be operated at variable capacities (e.g., operating a chiller at 10% capacity or 60% capacity) according to an operating setpoint received from asset allocator 402. Asset allocator 402 can control the equipment of subplants 420 and storage 430 to adjust the amount of each resource purchased, consumed, and/or produced by system 400.

In some embodiments, asset allocator 402 minimizes the cost function while participating in PBDR programs, IBDR programs, or simultaneously in both PBDR and IBDR programs. For the IBDR programs, asset allocator 402 may use statistical estimates of past clearing prices, mileage ratios, and event probabilities to determine the revenue generation potential of selling stored energy to resource purchasers 441 or energy grid 442. For the PBDR programs, asset allocator 402 may use predictions of ambient conditions, facility thermal loads, and thermodynamic models of installed equipment to estimate the resource consumption of subplants 420. Asset allocator 402 may use predictions of the resource consumption to monetize the costs of running the equipment.

Asset allocator 402 may automatically determine (e.g., without human intervention) a combination of PBDR and/or IBDR programs in which to participate over the optimization horizon in order to maximize economic value. For example, asset allocator 402 may consider the revenue generation potential of IBDR programs, the cost reduction potential of PBDR programs, and the equipment maintenance/replacement costs that would result from participating in various combinations of the IBDR programs and PBDR programs. Asset allocator 402 may weigh the benefits of participation against the costs of participation to determine an optimal combination of programs in which to participate. Advantageously, this allows asset allocator 402 to determine an optimal set of control decisions that maximize the overall value of operating asset allocation system 400.

In some embodiments, asset allocator 402 optimizes the cost function J(x) subject to the following constraint, which guarantees the balance between resources purchased, produced, discharged, consumed, and requested over the optimization horizon:

${{{\sum\limits_{sources}{{purchas}e_{{resource},{time}}}} + {\sum\limits_{subplants}{{produces}\left( {x_{{internal},{time}},x_{{external},{time}},v_{{uncontrolled},{time}}} \right)}} - {\sum\limits_{subplants}{{consumes}\left( {x_{{internal},{time}},x_{{external},{time}},v_{{uncontrolled},{time}}} \right)}} + {\sum\limits_{storages}{{discharges}_{resource}\left( {x_{{internal},{time}},x_{{external},{time}}} \right)}} - {\sum\limits_{sinks}{requests}_{resource}}} = {0{\forall{resources}}}},{\forall{{time} \in {horizon}}}$

where x_(internal,time) includes internal decision variables (e.g., load allocated to each component of asset allocation system 400), x_(external,time) includes external decision variables (e.g., condenser water return temperature or other shared variables across subplants 420), and v_(uncontrolled,time) includes uncontrolled variables (e.g., weather conditions).

The first term in the previous equation represents the total amount of each resource (e.g., electricity, water, natural gas, etc.) purchased from each source 410 over the optimization horizon. The second and third terms represent the total production and consumption of each resource by subplants 420 over the optimization horizon. The fourth term represents the total amount of each resource discharged from storage 430 over the optimization horizon. Positive values indicate that the resource is discharged from storage 430, whereas negative values indicate that the resource is charged or stored. The fifth term represents the total amount of each resource requested by sinks 440 over the optimization horizon. Accordingly, this constraint ensures that the total amount of each resource purchased, produced, or discharged from storage 430 is equal to the amount of each resource consumed, stored, or provided to sinks 440.

In some embodiments, additional constraints exist on the regions in which subplants 420 can operate. Examples of such additional constraints include the acceptable space (i.e., the feasible region) for the decision variables given the uncontrolled conditions, the maximum amount of a resource that can be purchased from a given source 410, and any number of plant-specific constraints that result from the mechanical design of the plant. These additional constraints can be generated and imposed by operational domain module 904 (described in greater detail with reference to FIGS. 9 and 12 ).

Asset allocator 402 may include a variety of features that enable the application of asset allocator 402 to nearly any central plant, central energy facility, combined heating and cooling facility, or combined heat and power facility. These features include broadly applicable definitions for subplants 420, sinks 440, storage 430, and sources 410; multiples of the same type of subplant 420 or sink 440; subplant resource connections that describe which subplants 420 can send resources to which sinks 440 and at what efficiency; subplant minimum turndown into the asset allocation optimization; treating electrical energy as any other resource that must be balanced; constraints that can be commissioned during runtime; different levels of accuracy at different points in the horizon; setpoints (or other decisions) that are shared between multiple subplants included in the decision vector; disjoint subplant operation regions; incentive based electrical energy programs; and high level airside models. Incorporation of these features may allow asset allocator 402 to support a majority of the central energy facilities that will be seen in the future. Additionally, it will be possible to rapidly adapt to the inclusion of new subplant types. Some of these features are described in greater detail below.

Broadly applicable definitions for subplants 420, sinks 440, storage 430, and sources 410 allow each of these components to be described by the mapping from decision variables to resources consume and resources produced. Resources and other components of system 400 do not need to be “typed,” but rather can be defined generally. The mapping from decision variables to resource consumption and production can change based on extrinsic conditions. Asset allocator 420 can solve the optimization problem by simply balancing resource use and can be configured to solve in terms of consumed resource 1, consumed resource 2, produced resource 1, etc., rather than electricity consumed, water consumed, and chilled water produced. Such an interface at the high level allows for the mappings to be injected into asset allocation system 400 rather than needing them hard coded. Of course, “typed” resources and other components of system 400 can still exist in order to generate the mapping at run time, based on equipment out of service.

Incorporating multiple subplants 420 or sinks 440 of the same type allows for modeling the interconnections between subplants 420, sources 410, storage 430, and sinks 440. This type of modeling describes which subplants 420 can use resource from which sources 410 and which subplants 420 can send resources to which sinks 440. This can be visualized as a resource connection matrix (i.e., a directed graph) between the subplants 420, sources 410, sinks 440, and storage 430. Extending this concept, it is possible to include costs for delivering the resource along a connection and also, efficiencies of the transmission (e.g., amount of energy that makes it to the other side of the connection).

In some instances, constraints arise due to mechanical problems after an energy facility has been built. Accordingly, these constraints are site specific and are often not incorporated into the main code for any of subplants 420 or the high level problem itself. Commissioned constraints allow for such constraints to be added without software updates during the commissioning phase of the project. Furthermore, if these additional constraints are known prior to the plant build, they can be added to the design tool run. This would allow the user to determine the cost of making certain design decisions.

Incentive programs often require the reservation of one or more assets for a period of time. In traditional systems, these assets are typically turned over to alternative control, different than the typical resource price based optimization. Advantageously, asset allocator 402 can be configured to add revenue to the cost function per amount of resource reserved. Asset allocator 402 can then make the reserved portion of the resource unavailable for typical price based cost optimization. For example, asset allocator 402 can reserve a portion of a battery asset for frequency response. In this case, the battery can be used to move the load or shave the peak demand, but can also be reserved to participate in the frequency response program.

Central Plant Controller

Referring now to FIG. 5 , a block diagram of a central plant controller 500 in which asset allocator 402 can be implemented is shown, according to an exemplary embodiment. In various embodiments, central plant controller 500 can be configured to monitor and control central plant 200, asset allocation system 400, and various components thereof (e.g., sources 410, subplants 420, storage 430, sinks 440, etc.). Central plant controller 500 is shown providing control decisions to a building management system (BMS) 506. The control decisions provided to BMS 506 may include resource purchase amounts for sources 410, setpoints for subplants 420, and/or charge/discharge rates for storage 430. In other embodiments, the central plant controller is configured in a planning tool implementation in which an operation of the central plant is planned over an optimization period (e.g., 1 year) for use in planning, operational decision-making, budgeting, planning for purchase of new assets, etc.

In some embodiments, BMS 506 is the same or similar to the BMS described with reference to FIG. 1 . BMS 506 may be configured to monitor conditions within a controlled building or building zone. For example, BMS 506 may receive input from various sensors (e.g., temperature sensors, humidity sensors, airflow sensors, voltage sensors, etc.) distributed throughout the building and may report building conditions to central plant controller 500. Building conditions may include, for example, a temperature of the building or a zone of the building, a power consumption (e.g., electric load) of the building, a state of one or more actuators configured to affect a controlled state within the building, or other types of information relating to the controlled building. BMS 506 may operate subplants 420 and storage 430 to affect the monitored conditions within the building and to serve the thermal energy loads of the building.

BMS 506 may receive control signals from central plant controller 500 specifying on/off states, charge/discharge rates, and/or setpoints for the subplant equipment. BMS 506 may control the equipment (e.g., via actuators, power relays, etc.) in accordance with the control signals provided by central plant controller 500. For example, BMS 506 may operate the equipment using closed loop control to achieve the setpoints specified by central plant controller 500. In various embodiments, BMS 506 may be combined with central plant controller 500 or may be part of a separate building management system. According to an exemplary embodiment, BMS 506 is a METASYS® brand building management system, as sold by Johnson Controls, Inc.

Central plant controller 500 may monitor the status of the controlled building using information received from BMS 506. Central plant controller 500 may be configured to predict the thermal energy loads (e.g., heating loads, cooling loads, etc.) of the building for plurality of time steps in an optimization period (e.g., using weather forecasts from a weather service 504). Central plant controller 500 may also predict the revenue generation potential of incentive based demand response (IBDR) programs using an incentive event history (e.g., past clearing prices, mileage ratios, event probabilities, etc.) from incentive programs 502. Central plant controller 500 may generate control decisions that optimize the economic value of operating central plant 200 over the duration of the optimization period subject to constraints on the optimization process (e.g., energy balance constraints, load satisfaction constraints, etc.). The optimization process performed by central plant controller 500 is described in greater detail below.

In some embodiments, central plant controller 500 is integrated within a single computer (e.g., one server, one housing, etc.). In various other exemplary embodiments, central plant controller 500 can be distributed across multiple servers or computers (e.g., that can exist in distributed locations). In another exemplary embodiment, central plant controller 500 may integrated with a smart building manager that manages multiple building systems and/or combined with BMS 506.

Central plant controller 500 is shown to include a communications interface 536 and a processing circuit 507. Communications interface 536 may include wired or wireless interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with various systems, devices, or networks. For example, communications interface 536 may include an Ethernet card and port for sending and receiving data via an Ethernet-based communications network and/or a WiFi transceiver for communicating via a wireless communications network. Communications interface 536 may be configured to communicate via local area networks or wide area networks (e.g., the Internet, a building WAN, etc.) and may use a variety of communications protocols (e.g., BACnet, IP, LON, etc.).

Communications interface 536 may be a network interface configured to facilitate electronic data communications between central plant controller 500 and various external systems or devices (e.g., BMS 506, subplants 420, storage 430, sources 410, etc.). For example, central plant controller 500 may receive information from BMS 506 indicating one or more measured states of the controlled building (e.g., temperature, humidity, electric loads, etc.) and one or more states of subplants 420 and/or storage 430 (e.g., equipment status, power consumption, equipment availability, etc.). Communications interface 536 may receive inputs from BMS 506, subplants 420, and/or storage 430 and may provide operating parameters (e.g., on/off decisions, setpoints, etc.) to subplants 420 and storage 430 via BMS 506. The operating parameters may cause subplants 420 and storage 430 to activate, deactivate, or adjust a setpoint for various devices thereof.

Still referring to FIG. 5 , processing circuit 507 is shown to include a processor 508 and memory 510. Processor 508 may be a general purpose or specific purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable processing components. Processor 508 may be configured to execute computer code or instructions stored in memory 510 or received from other computer readable media (e.g., CDROM, network storage, a remote server, etc.).

Memory 510 may include one or more devices (e.g., memory units, memory devices, storage devices, etc.) for storing data and/or computer code for completing and/or facilitating the various processes described in the present disclosure. Memory 510 may include random access memory (RAM), read-only memory (ROM), hard drive storage, temporary storage, non-volatile memory, flash memory, optical memory, or any other suitable memory for storing software objects and/or computer instructions. Memory 510 may include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. Memory 510 may be communicably connected to processor 508 via processing circuit 507 and may include computer code for executing (e.g., by processor 508) one or more processes described herein.

Memory 510 is shown to include a building status monitor 524. Central plant controller 500 may receive data regarding the overall building or building space to be heated or cooled by system 400 via building status monitor 524. In an exemplary embodiment, building status monitor 524 may include a graphical user interface component configured to provide graphical user interfaces to a user for selecting building requirements (e.g., overall temperature parameters, selecting schedules for the building, selecting different temperature levels for different building zones, etc.).

Central plant controller 500 may determine on/off configurations and operating setpoints to satisfy the building requirements received from building status monitor 524. In some embodiments, building status monitor 524 receives, collects, stores, and/or transmits cooling load requirements, building temperature setpoints, occupancy data, weather data, energy data, schedule data, and other building parameters. In some embodiments, building status monitor 524 stores data regarding energy costs, such as pricing information available from sources 410 (energy charge, demand charge, etc.).

Still referring to FIG. 5 , memory 510 is shown to include a load/rate predictor 522. Load/rate predictor 522 may be configured to predict the thermal energy loads (

) of the building or campus for each time step k (e.g., k=1 . . . n) of an optimization period. Load/rate predictor 522 is shown receiving weather forecasts from a weather service 504. In some embodiments, load/rate predictor 522 predicts the thermal energy loads

_(k) as a function of the weather forecasts. In some embodiments, load/rate predictor 522 uses feedback from BMS 506 to predict loads

_(k). Feedback from BMS 506 may include various types of sensory inputs (e.g., temperature, flow, humidity, enthalpy, etc.) or other data relating to the controlled building (e.g., inputs from a HVAC system, a lighting control system, a security system, a water system, etc.).

In some embodiments, load/rate predictor 522 receives a measured electric load and/or previous measured load data from BMS 506 (e.g., via building status monitor 524). Load/rate predictor 522 may predict loads

_(k) as a function of a given weather forecast ({circumflex over (ϕ)}_(w)), a day type (day), the time of day (t), and previous measured load data (Y_(k-1)). Such a relationship is expressed in the following equation:

_(k) =f({circumflex over (ϕ)}_(w),day,t|Y _(k-1))

In some embodiments, load/rate predictor 522 uses a deterministic plus stochastic model trained from historical load data to predict loads

_(k). Load/rate predictor 522 may use any of a variety of prediction methods to predict loads

_(k) (e.g., linear regression for the deterministic portion and an AR model for the stochastic portion). Load/rate predictor 522 may predict one or more different types of loads for the building or campus. For example, load/rate predictor 522 may predict a hot water load

_(Hot,k) and a cold water load

_(Cold,k) for each time step k within the prediction window. In some embodiments, load/rate predictor 522 makes load/rate predictions using the techniques described in U.S. patent application Ser. No. 14/717,593.

Load/rate predictor 522 is shown receiving utility rates from sources 410. Utility rates may indicate a cost or price per unit of a resource (e.g., electricity, natural gas, water, etc.) provided by sources 410 at each time step k in the prediction window. In some embodiments, the utility rates are time-variable rates. For example, the price of electricity may be higher at certain times of day or days of the week (e.g., during high demand periods) and lower at other times of day or days of the week (e.g., during low demand periods). The utility rates may define various time periods and a cost per unit of a resource during each time period. Utility rates may be actual rates received from sources 410 or predicted utility rates estimated by load/rate predictor 522.

In some embodiments, the utility rates include demand charges for one or more resources provided by sources 410. A demand charge may define a separate cost imposed by sources 410 based on the maximum usage of a particular resource (e.g., maximum energy consumption) during a demand charge period. The utility rates may define various demand charge periods and one or more demand charges associated with each demand charge period. In some instances, demand charge periods may overlap partially or completely with each other and/or with the prediction window. Advantageously, demand response optimizer 530 may be configured to account for demand charges in the high level optimization process performed by asset allocator 402. Sources 410 may be defined by time-variable (e.g., hourly) prices, a maximum service level (e.g., a maximum rate of consumption allowed by the physical infrastructure or by contract) and, in the case of electricity, a demand charge or a charge for the peak rate of consumption within a certain period. Load/rate predictor 522 may store the predicted loads

and the utility rates in memory 510 and/or provide the predicted loads

and the utility rates to demand response optimizer 530.

Still referring to FIG. 5 , memory 510 is shown to include an incentive estimator 520. Incentive estimator 520 may be configured to estimate the revenue generation potential of participating in various incentive-based demand response (IBDR) programs. In some embodiments, incentive estimator 520 receives an incentive event history from incentive programs 502. The incentive event history may include a history of past IBDR events from incentive programs 502. An IBDR event may include an invitation from incentive programs 502 to participate in an IBDR program in exchange for a monetary incentive. The incentive event history may indicate the times at which the past IBDR events occurred and attributes describing the IBDR events (e.g., clearing prices, mileage ratios, participation requirements, etc.). Incentive estimator 520 may use the incentive event history to estimate IBDR event probabilities during the optimization period.

Incentive estimator 520 is shown providing incentive predictions to demand response optimizer 530. The incentive predictions may include the estimated IBDR probabilities, estimated participation requirements, an estimated amount of revenue from participating in the estimated IBDR events, and/or any other attributes of the predicted IBDR events. Demand response optimizer 530 may use the incentive predictions along with the predicted loads

and utility rates from load/rate predictor 522 to determine an optimal set of control decisions for each time step within the optimization period.

Still referring to FIG. 5 , memory 510 is shown to include a demand response optimizer 530. Demand response optimizer 530 may perform a cascaded optimization process to optimize the performance of asset allocation system 400. For example, demand response optimizer 530 is shown to include asset allocator 402 and a low level optimizer 534. Asset allocator 402 may control an outer (e.g., subplant level) loop of the cascaded optimization. Asset allocator 402 may determine an optimal set of control decisions for each time step in the prediction window in order to optimize (e.g., maximize) the value of operating asset allocation system 400. Control decisions made by asset allocator 402 may include, for example, load setpoints for each of subplants 420, charge/discharge rates for each of storage 430, resource purchase amounts for each type of resource purchased from sources 410, and/or an amount of each resource sold to energy purchasers 504. In other words, the control decisions may define resource allocation at each time step. The control decisions made by asset allocator 402 are based on the statistical estimates of incentive event probabilities and revenue generation potential for various IBDR events as well as the load and rate predictions.

Low level optimizer 534 may control an inner (e.g., equipment level) loop of the cascaded optimization. Low level optimizer 534 may determine how to best run each subplant at the load setpoint determined by asset allocator 402. For example, low level optimizer 534 may determine on/off states and/or operating setpoints for various devices of the subplant equipment in order to optimize (e.g., minimize) the energy consumption of each subplant while meeting the resource allocation setpoint for the subplant. In some embodiments, low level optimizer 534 receives actual incentive events from incentive programs 502. Low level optimizer 534 may determine whether to participate in the incentive events based on the resource allocation set by asset allocator 402. For example, if insufficient resources have been allocated to a particular IBDR program by asset allocator 402 or if the allocated resources have already been used, low level optimizer 534 may determine that asset allocation system 400 will not participate in the IBDR program and may ignore the IBDR event. However, if the required resources have been allocated to the IBDR program and are available in storage 430, low level optimizer 534 may determine that system 400 will participate in the IBDR program in response to the IBDR event. The cascaded optimization process performed by demand response optimizer 530 is described in greater detail in U.S. patent application Ser. No. 15/247,885.

In some embodiments, low level optimizer 534 generates and provides subplant curves to asset allocator 402. Each subplant curve may indicate an amount of resource consumption by a particular subplant (e.g., electricity use measured in kW, water use measured in L/s, etc.) as a function of the subplant load. In some embodiments, low level optimizer 534 generates the subplant curves by running the low level optimization process for various combinations of subplant loads and weather conditions to generate multiple data points. Low level optimizer 534 may fit a curve to the data points to generate the subplant curves. In other embodiments, low level optimizer 534 provides the data points asset allocator 402 and asset allocator 402 generates the subplant curves using the data points. Asset allocator 402 may store the subplant curves in memory for use in the high level (i.e., asset allocation) optimization process.

In some embodiments, the subplant curves are generated by combining efficiency curves for individual devices of a subplant. A device efficiency curve may indicate the amount of resource consumption by the device as a function of load. The device efficiency curves may be provided by a device manufacturer or generated using experimental data. In some embodiments, the device efficiency curves are based on an initial efficiency curve provided by a device manufacturer and updated using experimental data. The device efficiency curves may be stored in equipment models 518. For some devices, the device efficiency curves may indicate that resource consumption is a U-shaped function of load. Accordingly, when multiple device efficiency curves are combined into a subplant curve for the entire subplant, the resultant subplant curve may be a wavy curve. The waves are caused by a single device loading up before it is more efficient to turn on another device to satisfy the subplant load.

Still referring to FIG. 5 , memory 510 is shown to include a subplant control module 528. Subplant control module 528 may store historical data regarding past operating statuses, past operating setpoints, and instructions for calculating and/or implementing control parameters for subplants 420 and storage 430. Subplant control module 528 may also receive, store, and/or transmit data regarding the conditions of individual devices of the subplant equipment, such as operating efficiency, equipment degradation, a date since last service, a lifespan parameter, a condition grade, or other device-specific data. Subplant control module 528 may receive data from subplants 420, storage 430, and/or BMS 506 via communications interface 536. Subplant control module 528 may also receive and store on/off statuses and operating setpoints from low level optimizer 534.

Data and processing results from demand response optimizer 530, subplant control module 528, or other modules of central plant controller 500 may be accessed by (or pushed to) monitoring and reporting applications 526. Monitoring and reporting applications 526 may be configured to generate real time “system health” dashboards that can be viewed and navigated by a user (e.g., a system engineer). For example, monitoring and reporting applications 526 may include a web-based monitoring application with several graphical user interface (GUI) elements (e.g., widgets, dashboard controls, windows, etc.) for displaying key performance indicators (KPI) or other information to users of a GUI. In addition, the GUI elements may summarize relative energy use and intensity across energy storage systems in different buildings (real or modeled), different campuses, or the like. Other GUI elements or reports may be generated and shown based on available data that allow users to assess performance across one or more energy storage systems from one screen. The user interface or report (or underlying data engine) may be configured to aggregate and categorize operating conditions by building, building type, equipment type, and the like. The GUI elements may include charts or histograms that allow the user to visually analyze the operating parameters and power consumption for the devices of the energy storage system.

Still referring to FIG. 5 , central plant controller 500 may include one or more GUI servers, web services 512, or GUI engines 514 to support monitoring and reporting applications 526. In various embodiments, applications 526, web services 512, and GUI engine 514 may be provided as separate components outside of central plant controller 500 (e.g., as part of a smart building manager). Central plant controller 500 may be configured to maintain detailed historical databases (e.g., relational databases, XML, databases, etc.) of relevant data and includes computer code modules that continuously, frequently, or infrequently query, aggregate, transform, search, or otherwise process the data maintained in the detailed databases. Central plant controller 500 may be configured to provide the results of any such processing to other databases, tables, XML files, or other data structures for further querying, calculation, or access by, for example, external monitoring and reporting applications.

Central plant controller 500 is shown to include configuration tools 516. Configuration tools 516 can allow a user to define (e.g., via graphical user interfaces, via prompt-driven “wizards,” etc.) how central plant controller 500 should react to changing conditions in the energy storage subsystems. In an exemplary embodiment, configuration tools 516 allow a user to build and store condition-response scenarios that can cross multiple energy storage system devices, multiple building systems, and multiple enterprise control applications (e.g., work order management system applications, entity resource planning applications, etc.). For example, configuration tools 516 can provide the user with the ability to combine data (e.g., from subsystems, from event histories) using a variety of conditional logic. In varying exemplary embodiments, the conditional logic can range from simple logical operators between conditions (e.g., AND, OR, XOR, etc.) to pseudo-code constructs or complex programming language functions (allowing for more complex interactions, conditional statements, loops, etc.). Configuration tools 516 can present user interfaces for building such conditional logic. The user interfaces may allow users to define policies and responses graphically. In some embodiments, the user interfaces may allow a user to select a pre-stored or pre-constructed policy and adapt it or enable it for use with their system.

Various other implementations of the cost functions, optimization processes, controllers, etc. described above are also possible. For example, the systems and methods described herein may be implemented with any combination of the various features described in U.S. patent application Ser. No. 15/405,236, filed Jan. 12, 2017; U.S. patent application Ser. No. 15/405,234, filed Jan. 12, 2017; U.S. patent application Ser. No. 15/429,962, filed Feb. 7, 2017; U.S. patent application Ser. No. 15/473,496, filed Mar. 29, 2017; U.S. patent application Ser. No. 15/616,616, filed Jun. 7, 2017; and U.S. patent application Ser. No. 16/115,290, filed Aug. 28, 2018. These applications are incorporated by reference herein in their entireties.

Validation and Control Using Expert Subplant Models

Referring generally to FIGS. 6-8 , methods for using expert subplant models to estimate output values of dependent variables relating to subplant operation in a central plant are shown, according or to exemplary embodiments. Subplant operation can be inherently non-linear and/or discontinuous, and can be difficult or impossible to model using analytic equations (e.g., mathematical functions), especially where multiple independent and dependent variables are involved. To model subplants with such behavior, expert models can be used which map discrete, numerical values of independent variables to discrete, numerical values of dependent variables, as detailed below. However, the independent and dependent variables can be continuous (for example representing physical conditions such as temperature that are inherently continuous in nature), such that a discrete set of values in an expert model cannot directly capture every possible value of the variables. The systems and methods described herein allow for using expert models to predict subplant behavior while dealing with this challenge.

Referring now to FIG. 6 , a flowchart of a process 600 for achieving control of a subplant of validation of subplant performance using expert models is shown, according to some embodiments. In some embodiments, the process 600 can be executed by the central plant controller 500 of FIG. 5 , for example using the expert models 516, monitoring and reporting applications 526, demand response optimizer 530, and/or subplant control module 528, for example.

At step 602, an expert model characterizing subplant operating using a map of independent data to dependent data is obtained. The independent data can include a plurality of discrete values for independent variables (e.g., inputs to the expert model), and the dependent data can include a plurality of discrete values for dependent variables (e.g., outputs of the expert model). The dependent variables represent traits, conditions, operating parameters, etc. of the subplant which are dependent upon the independent variables or otherwise related to the independent variables. In the notation used in the following description, the expert model includes n independent variables and m dependent variables. The independent and dependent variables may represent the resources consumed or produced by a subplant or equipment thereof as well as other outside variables that affects the relationship between resource consumption and resource production. As a non-exhaustive list, the independent variables and/or dependent variables can represent electricity or other power consumption, water consumption, natural gas consumption, steam production, chilled water production, dry bulb or wet bulb temperature (e.g., supply water temperature, supply air temperature, superheat temperature, indoor air temperature, etc.), air flow rate, fluid flow rate, compressor speed, fan speed, percentage of equipment capacity, weather data, humidity, time of day, etc. as may be suitable to characterize different types of subplants in different central plants.

As a first example, the following table shows an example expert model for a chiller tower subplant. In the model below, the chilled water production (units of Watts) is an independent variable, as is wetbulb temperature (e.g., weather data indicating outdoor air temperature). Electricity consumption and water flow rate (water consumption) are the dependent variables. The row of “NaN”s signifies that there are two operating regions. In this model the first region is an “off” region, where the Chillers and Towers are not running (above the NaNs in the table). The second region (below the NaNs in the table) is the “on” region, where the minimum turndowns and capacities are defined, as are the relationships between the dependent and independent data:

ChilledWater Water Electricity Wetbulb [W] [m{circumflex over ( )}3/hr] [W] [deg C.] 0 0 0 −45.5556 0 0 0 93.333 NaN NaN NaN NaN 175850 0.29678112 26471.82758 −45.5556 175850 0.29678112 26471.82758 93.333 1758500 2.9678112 264718.2758 −45.5556 1758500 2.9678112 264718.2758 93.333

As a second example, the following table shows an example expert model for a precooled combustion turbine supplant. Electricity production, steam production and dry bulb temperature are the independent variables, while natural gas consumption and chilled water consumption are dependent variables. As above, the row of NaNs separates an “off” region from an “on” region for the precooled combustion turbine supplant:

Electricity Steam NaturalGas ChilledWater Drybulb [W] [tonnes/hr] [W] [W] [deg C.] 0 0 0 0 −50 0 0 0 0 100 NaN NaN NaN NaN NaN 3500000 8.5874042 15057974.86 0 −50 5000000 10.74715099 19143221.63 0 −50 3500000 8.5874042 15057974.86 0 −20 5000000 10.74715099 19143221.63 0 −20 3500000 8.627317905 15078663.03 0 −10 5000000 10.81190281 19206570.85 0 −10 3500000 8.661153999 15093269.13 0 0 5000000 10.86853772 19263056.54 0 0 3500000 8.685863789 15098803.94 0 10 4991300 10.90426128 19284594.4 0 10 3500000 8.685863789 15098803.94 0 20 4991300 10.90426128 19284594.4 0 20 3500000 8.689820042 15096041.61 0 30 4875701.156 10.79988795 18972626.58 0 30 3500000 8.689820042 15096041.61 0 100 4875701.156 10.79988795 18972626.58 0 100 3500000 0.045858228 17988685.56 0 −50 5000000 0.045858228 22073932.34 0 −50 3500000 0.045858228 17988685.56 0 −20 5000000 0.045858228 22073932.34 0 −20 3500000 0.045858228 18009373.73 0 −10 5000000 0.045858228 22137281.56 0 −10 3500000 0.045858228 18023979.83 0 0 5000000 0.045858228 22193767.24 0 0 3500000 0.045858228 18029514.64 0 10 4991300 0.045858228 22215305.1 0 10 3500000 0.045858228 18029514.64 0 20 4991300 0.045858228 22215305.1 0 20 3500000 0.045858228 18026752.31 0 30 4875701.156 0.045858228 21903337.29 0 30 3500000 0.045858228 18026752.31 0 100 4875701.156 0.045858228 21903337.29 0 100 3500000 36.10234128 35269772.81 0 −50 5000000 38.26208807 39355019.59 0 −50 3500000 36.10234128 35269772.81 0 −20 5000000 38.26208807 39355019.59 0 −20 3500000 36.14225499 35290460.96 0 −10 5000000 38.32688575 39418368.8 0 −10 3500000 36.17609108 35305067.07 0 0 5000000 38.3834748 39474854.47 0 0 3500000 36.20080087 35310601.89 0 10 4991300 38.41919836 39496392.35 0 10 3500000 36.20080087 35310601.89 0 20 4991300 38.41919836 39496392.35 0 20 3500000 36.20475712 35307839.55 0 30 4875701.156 38.31482504 39184424.53 0 30 3500000 36.20475712 35307839.55 0 100 4875701.156 38.31482504 39184424.53 0 100

Process 600 and step 602 contemplate that an expert model can have any number n of independent variables and any number m of dependent variables (i.e., any number of total columns as formatted in the tables above) as well as any number of sets of values mapping from the independent variables to the dependent variables (i.e., any number of rows as formatted in the tables above). As can be seen, even in the second example which includes a larger number of rows, the points in the multiple-dimensional modeling space of the expert model are discrete points, whereas variables can be continuous and can take on values between the points included in the expert models. For example, the number of rows in the models above may be selected to optimally reduce memory requirements and improve computing efficiency associated with storage and use of an expert model while providing sufficient information to generate accurate estimates.

At step 604, input values for independent variables represented in the independent data are obtained. For example, the input values can include measured values from real plant operations. As another example, the input values can include predicted or simulated values of the independent variables. In some embodiments, the input values are selected as part of a test or evaluation experiment, for example a validation or verification experiment. The input values can include one value for each independent variable (i.e., n values) corresponding to a shared time step (i.e., the same point in time).

At step 606, a spatial relationship between the input data and the expert model in an n-dimensional modeling space is determined. The n-dimensional modeling space includes a dimension corresponding to each independent variable, so that the values of the independent variables in the input data can be geometrically compared to values of the independent variables included in the expert model. In some embodiments, determining the geometric relationship includes determining vertices of a smallest n-dimensional shape which contains the point defined by the input data while the vertices are defined by points included in the expert model. For example, step 606 can include selecting the closest point of the expert model to the input data in each of 2^(n) directions, thereby selecting 2^(n) vertices defining an n-dimensional shape that surrounds the input data (e.g., eight vertices defining a three-dimensional box if n=3). An example embodiment for defining and using a geometric relationship between the input data the expert model is described below in additional detail with reference to FIGS. 7-8 .

At step 608, a reduced expert model is generated based on the spatial relationship between the input data and the expert model. For example, the reduced expert model can include a portion of the expert model determined to be spatially close to the input data in step 606, while a remainder of the expert model is ignored. In some examples, the reduced expert model includes 2^(n) sets of independent and dependent values (i.e., 2^(n) rows in the format of the example tables above).

At step 610, output data indicating estimated values of the dependent variables are generated using the reduced expert model and the input data. For example, an interpolation can be performed using the reduced expert model to estimate values of the dependent variables based on the remaining values of the dependent values in the reduced expert model (e.g. a weighted average thereof).

Process 600 can include initiating an automated action using the output data (output values of the dependent variables), for example as in the examples of step 612 and/or 614. At step 612, a validation process is executed using the output data. For example, the output data may be used by in analytics calculations do determine energy or resource utilization information, estimated operational costs, generate key performance indicators, etc. for the plant or subplant. In some embodiments, the validation process includes using the output data to estimating costs or energy savings that result from implementation of an control optimization procedure for the plant or subplant e.g., implementation of the control process described above with reference to FIGS. 4-5 . Step 612 can include generating and displaying a graphical user interface on a user display device that includes the output data and/or one or more metrics, estimations, visualizations, etc. generated using the output data.

At step 614, in addition to or as an alternative to step 612, the output data is used to control the subplant. For example, the output data may be used in a predictive control process, where the output data indicates a predicted future operation of the subplant based on predicted or expected future input values. A predictive optimization can be performed using the output data, for example according to the systems and methods described above with reference to FIGS. 4-5 . As another example, the output data may be used to control the subplant to achieve a setpoint indicating a desired or intended value for a dependent variable. Various control approaches are possible which use the output data to control the subplant.

Referring now to FIG. 7 , a flowchart of a process 700 for outputting estimated values of dependent data based on user provided independent data and an expert model is shown, according to an example embodiment. Process 700 can be used to execute process 600 in some examples. In some embodiments, process 700 can be executed by the central plant controller 500 of FIG. 5 , for example using the expert models 516, monitoring and reporting applications 526, demand response optimizer 530, and/or subplant control module 528, for example.

At step 702, a user provides independent data. The independent data can be input via user interface, uploaded via a communications network, etc. In some embodiments, the independent data defines conditions for a validation or verification experiment, for example an experiment design to demonstrate an effect operating a central plant according to an optimized control strategy (e.g., an optimized asset allocation as described above with reference to FIGS. 4-5 ) relative to a baseline or non-optimized control scheme.

At step 704, a determination is made as to what region of the expert model the independent data is in. As discussed above, the expert model can include multiple regions for multiple operating states of a subplant, for example an “on” region and an “off” region. In the example tables give above, the regions are separated by a row of NaN values. The determination in step 704 can be made by comparing the values of the independent data to the limits (bounds) on each region in the expert model (e.g., the maximum and minimum values for each variable that falls in a given region).

At step 704, a determination is made as to whether the independent data is in a single region, i.e., whether all values of the independent variables are within the same region of the expert model. Step 704 amounts to a check on whether the independent data is a physically-possible condition for the equipment. If the data represents a physically-possible condition, the independent data will be in a single region of the expert model. If the data describes a physically-impossible condition, the independent data will not be in a single region. For example, a user may provide independent data in step 702 where one independent variable has a value that can only be achieved while a subplant is operating in an “on” state and a second independent variable has a value that can only be achieved while a subplant is operating in an “off” state, in which case the independent data describes a physically-impossible condition and the independent data is not in a single region (“No” at step 706). In such a scenario (i.e., when the independent data is not in a single region, process 706 proceeds to step 708 where a violation of the expert model is reported to a user. For example, step 708 can include generating an alert, error message, alarm, etc. and providing the alert, error message, alarm, etc. to the user.

If the independent data is in a single region of the expert model (“Yes” at step 706), the process 700 proceeds to step 710. In step 710, a determination is made as to whether the data is on an edge of the region. That is, the independent data is assessed to determine whether it falls on a boundary of a region, for example at the maximum or minimum values of the independent variables defining a region. Because of how the expert models are formulated, independent data at the boundary of a region can be treated differently and processed more efficiently, such that step 710 can be executed to identify such input data for different treatment. If the independent data is determined to fall on the boundary of the region (“Yes” at step 710), process 700 proceeds to step 712 where the point in the expert model having independent values closest to the independent data is identified, and the dependent data associated with that point is selected as the dependent data. Step 712 may include selecting a point on the boundary of the region, for example. Step 712 can include determining a distance from the independent data to some or all points of the expert model (e.g., in an n-dimensional modeling space), and then selecting the point associated with the shortest distance in step 712. Dependent data (i.e., values of dependent variables resulting from the values of the independent variables shown in the input data) is thereby estimated for points on a boundary of a region. As shown in FIG. 7 , step 712 can also be used to generate dependent data where the independent data is not in a single region (i.e., following step 708).

At step 714, a determination is made as to whether the problem can be solved linearly. In some embodiments, step 714 includes counting the number of variables in the expert model, and determining that the problem can be solved linearly when the expert model has one independent variable and one dependent variable, and when the region in which the independent data lies only includes two points of the expert model. In such a scenario, a linear model of y=mx+b can be defined using the two points and used to calculate the value of the dependent variable (i.e., a value of y) by inputting the value of the independent variable (i.e., a value of x). Step 714 is thereby included in process 700 to identify scenarios which can be dealt with using this relatively simple approach, so that other, more resource-intensive steps of process 700 can be bypassed in such scenarios. If a determination is made that the problem can be solved linearly (“Yes” at step 714), then process 700 proceeds to step 716 where the problem is solved linearly. For example, step 716 can include using a linear model (y=mx+b) to the define the problem from the expert model and then using the linear model to get a value for the dependent variable by inputting the value for the independent variable from the independent data.

If the problem cannot be solved linearly (“No” at step 714), the process 700 proceeds to step 718. In step 718, the smallest n-dimensional space surrounding the independent data is determined, for example using vector math. In particular, the smallest n-dimensional space surrounding the independent data can determined by defining vectors pointing outwardly from the independent data point in each of 2^(n) directions in the n-dimensional space, where each direction has a positive or negative value for each of the n dimensions. For the sake of illustration, the following table defines the eight directions in a three-dimensional space that can be used in an embodiment with three independent variables and a modeling space having three dimensions denoted as x, y, and z:

Dimension x Dimension y Dimension z + + + + + − + − + + − − − + + − + − − − + − − −

Each of the 2^(n) directions corresponds to a different subspace of the n-dimensional modeling space. Each of the 2^(n) subspaces is located in the corresponding direction from the independent data received in step 702. Each subspace has a vertex at the location of the independent data received in step 702 and extends outward from the location of the independent data in the corresponding direction. Step 718 may include using vector math to identify a point of the expert model closest to the independent data received in step —702 in each of the 2^(n) subspaces. For example, step 718 may include identifying 2^(n) points of the expert model, where each of the identified points exists in a different subspace of the 2^(n) subspaces and is the closest point in that subspace to the independent data received in step 702.

An example illustration of a 3-dimensional space vectors defined in 2³=8 dimensions is shown in FIG. 8 , according to an example scenario. FIG. 8 shows an illustration 800 including a input point 802 representing the location of the independent data in the modeling space and expert model points 804 representing the location of points in the expert model (i.e., values of the independent variables for which the expert model stores a map to values of dependent variables). FIG. 8 also shows vectors 806 pointing in each of the eight directions in the table above and extending outwardly from the input point 802. Each vector 806 points to the closest expert model point 804 in the given direction. Stated another way, step 718 can include searching each of 2^(n) sub-spaces (e.g., regions, quadrants, octants, etc. relative to the input point 802) for the closest expert model point 804 to the input point 802 in that region, thereby defining the vectors 806 shown in FIG. 8 . The closest of the expert model points 804 are then selected as defining the smallest n-dimensional space of the expert model surrounding the input independent data. For example, FIG. 8 shows an approximately-cube-shaped three-dimensional space surrounding the input independent data 802. It should be understood that FIG. 8 shows a three-dimensional example for ease of illustration, but that the approach of step 718 is defined generally and can handle any n-dimensional model (where n is an integer greater than or equal to one).

At step 720, the expert model is reduced to the smallest n-dimensional space determined in step 718. That is, a reduced expert model including only the vertices of the smallest n-dimensional space (i.e., the terminuses of the vertices generated in step 718) and the corresponding dependent data is obtained from the selected points of the expert model, while the rest of the expert model is ignored. In the example of FIG. 8 , for example, eight rows of an expert model formatted as in the example tables above would be retained as the reduced expert model.

At step 722, a determination is made as to whether, following reduction to the reduced expert model, the resulting problem can be solved linearly. For example, in some scenarios the reduction to the reduced expert model via steps 718 and 720 can reduce a problem which could not be solved linearly at step 714 to a problem that can now be solved linearly. Such a scenario may be a case involving one independent variable, one dependent variable, and input data in a region that includes multiple expert model points (multiple sets of input/output data). In such a scenario, the reduced expert model includes only two points which surround the independent variable in the expert model. Such a problem can be solved linearly (“Yes” at step 722), such that the process 700 will proceed to step 716 where the problem is solved linearly.

If a determination is made that the problem cannot be solved linearly (“No” at step 722), the process 700 will proceed to step 724. At step 724, an n-dimensional interpolation is performed to determine estimated values for the dependent variables based on the reduced expert model and the independent input data. Various approaches for n-dimensional interpolations (multidimensional interpolations) can be used, for example nearest-neighbor interpolation, kriging, inverse distance weighting, natural neighbor interpolation, spline interpolation, radial basis function interpolation, etc.

In some embodiments, the interpolation in step 724 ensures that the estimated values for the dependent variables generated by performing the interpolation have a smallest interpolated value in a region between the expert model points, i.e., minimized (smallest, etc.) relative to other possible results of the interpolation. An example is illustrated in FIG. 9 , where two independent variables and one dependent variable are represented by the three perpendicular axes of a three-dimensional graph 900, with an input data point 802 and the four closest model points 804 to the input data point 802 plotted in three-dimensional space, according to some embodiments. Any of the model points 804 may be located on the two-dimensional plane defined by the two independent variable axes or may be located above or below that two-dimensional plane, depending on the corresponding values of the dependent variable in each of the model points 804. In the example shown in FIG. 9 , the triangular surfaces formed by connecting the model points 804 form a tetrahedron in three-dimensional space.

Some interpolation techniques work by selecting two adjacent surfaces defined by the four model points 804 (e.g., two of the four triangular surfaces of the tetrahedron) and picking a point on that combination of surfaces corresponding to a projection of the input data point 802 on that combination of surfaces. However, different results will occur depending on which combination of surfaces is selected by the interpolation process. For example, projecting the input data point 802 onto a first surface or combination of the surfaces may result in a first value of the dependent variable, whereas projecting the input data point 802 onto a second surface or combination of the surfaces may result in a second different value of the dependent variable.

In order to cause the interpolation in step 724 to estimate a value of the dependent variable comparable to that which would result from an optimization process using the model points 804, the interpolation can be configured to select combination of planes which results in the lowest estimated value for the dependent variable(s). In the example shown, the interpolation can characterized as a selection of a point 902 on the plane connecting three model points 804 having the lowest values of the dependent variable. The selected point 902 may lie on the selected plane and may have independent variable coordinates matching the input data point 802. While the example shown in FIG. 9 includes two independent variables and one dependent variable to facilitate three-dimensional illustration, it should be understood that this approach is extendable to other dimensionalities and can be used with models having any number of independent and dependent variables. Such an interpolation can be characterized as including a minimization, maximization, optimization, or other algorithmic selection to cause the interpolation of step 724 to select appropriate value(s) for the one or more dependent variables which are most comparable to expected results of an optimization process using the expert model.

At step 726, the solved dependent data is output. The solved dependent data can be provided as an output of step 724, step 716, or step 712 as shown in FIG. 7 . Step 726 can include generating a graphical user interface including an indication, visualization, etc. of the solved dependent data. Step 726 can also include outputting the solved dependent data to a control optimization process that generates control signals for the subplant based at least in part on the dependent data from step 726. In some embodiments, step 726 can include causing the dependent data to be used to calculate energy savings estimates, energy usage estimates, other resource consumption or savings related estimates, etc. The dependent data can thus be used for to enable a variety of processes, for example as described for steps 612 and 614 of process 600.

Configuration of Exemplary Embodiments

The construction and arrangement of the systems and methods as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements can be reversed or otherwise varied and the nature or number of discrete elements or positions can be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps can be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions can be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure.

As utilized herein, the terms “approximately,” “about,” “substantially,” and similar terms are intended to have a broad meaning in harmony with the common and accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. It should be understood by those of skill in the art who review this disclosure that these terms are intended to allow a description of certain features described and claimed without restricting the scope of these features to the precise numerical ranges provided. Accordingly, these terms should be interpreted as indicating that insubstantial or inconsequential modifications or alterations of the subject matter described and are considered to be within the scope of the disclosure.

The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure can be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Embodiments within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions. 

What is claimed is:
 1. A central plant comprising: a plurality of subplants; circuitry configured to: obtain an expert model associated with a first subplant of the plurality of subplants, wherein the expert model comprises a map of values of one or more independent variables characterizing operation of the first subplant to one or more dependent variables characterizing operation of the first subplant; receive input data indicating input values for the independent variables; estimate outputs values for the one or more dependent variables associated with the input variables by: determining a spatial relationship between the input data and the expert model; reducing the expert model to a reduced model based on the spatial relationship; and performing an interpolation using the reduced model to generate the output values for the one or more dependent variables; and initiate an automated action using the output values.
 2. The central plant of claim 1, wherein determining the spatial relationship between the input data and the expert model comprises: defining a plurality of n-dimensional directions in coordinate system of the expert model, wherein n is a count of the independent variables; and determining a set of closest points of the expert model to the input data in the plurality of n-dimensional directions.
 3. The central plant of claim 2, wherein the plurality of n-dimensional directions consists of 2^(n) n-dimensional directions.
 4. The central plant of claim 2, wherein reduced model is defined by the set of the closest points of the expert model to the input data in the plurality of n-dimensional directions.
 5. The central plant of claim 1, further comprising generating a setpoint for the first subplant by performing an optimization of a predictive objective function using the output values.
 6. The central plant of claim 1, wherein the circuitry is configured to initiate the automated action by executing a validation procedure comprising collecting measurements while the first subplant operates in accordance with at least one of the input data and the output data and generating a report using the measurements, the input data, and the output data.
 7. The central plant of claim 6, further comprising a user display device, wherein the circuitry is further configured to cause the user device to display the report.
 8. The central plant of claim 1, wherein performing the interpolation comprises a step configured to minimize the output values relative to other possible outcomes of the interpolation.
 9. A method, comprising: obtaining an expert model associated with a first subplant of a central plant, wherein the expert model comprises a map of values of independent variables to one or more dependent variables; receiving input data indicating input values for the independent variables; estimating outputs values for the one or more dependent variables associated with the input variables by: determining a spatial relationship between the input data and the expert model; reducing the expert model to a reduced model based on the spatial relationship; and performing an interpolation using the reduced model to generate the output values for the one or more dependent variables; and initiating an automated action using the output values.
 10. The method of claim 9, wherein determining the spatial relationship between the input data and the expert model comprises: defining a plurality of n-dimensional directions in coordinate system of the expert model, wherein n is a count of the independent variables; and determining a set of closest points of the expert model to the input data in the plurality of n-dimensional directions.
 11. The method of claim 10, wherein the plurality of n-dimensional directions consists of 2^(n) n-dimensional directions.
 12. The method of claim 10, wherein reduced model is defined by the set of the closest points of the expert model to the input data in the plurality of n-dimensional directions.
 13. The method of claim 9, wherein initiating the automated action comprises generating a setpoint for the first subplant by performing an optimization of a predictive objective function using the output values.
 14. The method of claim 9, wherein initiating the automated action comprises executing a validation procedure comprising collecting measurements while the first subplant operates in accordance with at least one of the input data and the output data and generating a report using the measurements, the input data, and the output data.
 15. The method of claim 9, wherein performing the interpolation comprises a step configured to minimize the output values relative to other possible outcomes of the interpolation.
 16. One or more non-transitory computer-readable media storing program instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising: obtaining an expert model associated with a first subplant of a central plant, wherein the expert model comprises a map of values of independent variables to one or more dependent variables; receiving input data indicating input values for the independent variables; estimating outputs values for the one or more dependent variables associated with the input variables by: determining a spatial relationship between the input data and the expert model; reducing the expert model to a reduced model based on the spatial relationship; and performing an interpolation using the reduced model to generate the output values for the one or more dependent variables; and initiating an automated action using the output values.
 17. The non-transitory computer-readable media of claim 16, wherein determining the spatial relationship between the input data and the expert model comprises: defining a plurality of n-dimensional directions in coordinate system of the expert model, wherein n is a count of the independent variables; and determining a set of closest points of the expert model to the input data in the plurality of n-dimensional directions.
 18. The non-transitory computer-readable media of claim 17, wherein the plurality of n-dimensional directions consists of 2^(n) n-dimensional directions.
 19. The non-transitory computer-readable media of claim 18, wherein reduced model is defined by the set of the closest points of the expert model to the input data in the plurality of n-dimensional directions.
 20. The non-transitory computer-readable media of claim 16, wherein the operations further comprise generating a setpoint for the first subplant using the output values. 